I'm a little interested to see what happens to you during and after your MC. Is this your first time? Check out Hopinso's day 8 post. What's my point? It's not just your body you detox. But more than that, your boyfriend thing is where I'm going here.
It's one thing for him to "look out for your best interests" by giving his opinion. It's another thing for him to really put the pressure on you for doing something YOU want to do that HE does not want you to do AND for you to bend under that to avoid - confrontation, if you will.
You are entitle to do what you want, and in a healthy relationship, your partner will understand that. Though there might be a free exchange of ideas and opinions, there are no controlling behaviors.
Aside from that, there is the possibility that his reasons are NOT for your benefit, but more because you are taking steps to move forward while he is not. It's easier for him to rationalize his eating habits if YOUR are not doing something healthy, and (in his perception) throwing that healthy behavior in his face which forces him to be more conscious of what he is choosing to do. Pressure on you makes it easier for him.
But back to my first paragraph - I'm just wondering what will transpire for you as you detox - especially if you choose NOT to hide it from your boyfriend, which is the mentally healthier way to go - even though it could result in arguments and yes, a breakup.